Revealing the escape mechanism of three-dimensional orbits in a tidally limited star cluster

TL;DR

This study investigates the escape mechanisms of three-dimensional star orbits in a tidally limited star cluster, revealing how initial conditions and energy levels influence escape times and pathways.

Contribution

It provides a detailed numerical analysis of escape basins and times in a star cluster model, highlighting the impact of initial vertical position and energy on orbit behavior.

Findings

Most stars near the (x,y) plane are trapped in chaotic orbits for long periods.

Higher initial z-values lead to well-defined escape basins.

Escape rates increase near the critical escape energy.

Abstract

The aim of this work is to explore the escape process of three-dimensional orbits in a star cluster rotating around its parent galaxy in a circular orbit. The gravitational field of the cluster is represented by a smooth, spherically symmetric Plummer potential, while the tidal approximation was used to model the steady tidal field of the galaxy. We conduct a thorough numerical analysis distinguishing between regular and chaotic orbits as well as between trapped and escaping orbits, considering only unbounded motion for several energy levels. It is of particular interest to locate the escape basins towards the two exit channels and relate them with the corresponding escape times of the orbits. For this purpose, we split our investigation into three cases depending on the initial value of the $z$ coordinate which was used for launching the stars. The most noticeable finding is that the majority of stars initiated very close to the primary $(x,y)$ plane move in chaotic orbits and they remain trapped for vast time intervals, while orbits with relatively high values of $z_0$ on the other hand, form well-defined basins of escape. It was also observed, that for energy levels close to the critical escape energy the escape rates of orbits are large, while for much higher values of energy most of the orbits have low escape periods or they escape immediately to infinity. We hope our outcomes to be useful for a further understanding of the dissolution process and the escape mechanism in open star clusters.